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# If m and n are positive integers, what is the number of factors of

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6619
GMAT 1: 760 Q51 V42
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If m and n are positive integers, what is the number of factors of  [#permalink]

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10 Mar 2017, 02:15
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Difficulty:

15% (low)

Question Stats:

77% (00:46) correct 23% (01:20) wrong based on 84 sessions

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If m and n are positive integers, what is the number of factors of $$3^m7^n$$?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 13 Apr 2010 Posts: 89 Re: If m and n are positive integers, what is the number of factors of [#permalink] ### Show Tags 10 Mar 2017, 02:26 MathRevolution wrote: If m and n are positive integers, what is the number of factors of $$3^m7^n$$? A. mn+m+n B. m-n+1 C. (m-1)(n-1) D. (m+1)(n+1) E. mn I think , the question should read m and n are prime numbers then only we can get the total factors as (m+1)(n+1) giving answer as D . Example . 10^2 === > 5^2 . 2^2 giving total factors as 9 (1, 2 , 4, 5 , 10, 20, 25, 50, and 100 ) for 100. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6619 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m and n are positive integers, what is the number of factors of [#permalink] ### Show Tags 12 Mar 2017, 17:48 ==> The number of factors of $$3^m7^n$$ becomes (m+1)(n+1). The answer is D. Answer: _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If m and n are positive integers, what is the number of factors of  [#permalink]

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13 Mar 2017, 00:02
no of factors is given by (m+1)(n+1)
Target Test Prep Representative
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Posts: 2830
Re: If m and n are positive integers, what is the number of factors of  [#permalink]

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15 Mar 2017, 15:33
1
MathRevolution wrote:
If m and n are positive integers, what is the number of factors of $$3^m7^n$$?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn

To determine the total number of factors of a particular number, we add 1 to each exponent of the prime factors in the prime factorization of that number and multiply the resulting numbers together. For example, 12 = 2^2 * 3^1; thus 12 has (2 + 1)(1 + 1) = (3)(2) = 6 factors. Here the number is 3^m * 7^n, so it has a total of (m + 1)(n + 1) factors.

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Re: If m and n are positive integers, what is the number of factors of  [#permalink]

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21 Oct 2018, 18:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If m and n are positive integers, what is the number of factors of &nbs [#permalink] 21 Oct 2018, 18:57
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